Chapter SH, Problem 8.8MPS

(a)

To determine

To calculate: To write the equation in slope-intercept form

Answer to Problem 8.8MPS

Equation in slope-intercept form is $y=1.47x+14.7$

Explanation of Solution

Given information: At a depth of $30$ meters, a scuba diver

noted the pressure was $58.8$ pounds per square inch (psi). At a depth of $70$ meters, the pressure was $117.6$ psi

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Equation of line passing through the points given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given that at a depth of $30$ meters, a scuba diver noted the pressure was $58.8$ pounds per square inch (psi). At a depth of $70$ meters, the pressure was $117.6$ psi

Thus, points on the equation are

  $\left(30,58.8\right)$ and $\left(70,117.6\right)$

Equation of line passing through the points given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Substituting the values,

  $\begin{array}{l}y-58.8=\frac{117.6-58.8}{70-30}\left(x-30\right)\\ y-58.8=\frac{58.8}{40}\left(x-30\right)\\ y-58.8=1.47\left(x-30\right)\\ y-58.8=1.47x-44.1\\ y=1.47x-44.1+58.8\\ y=1.47x+14.7\end{array}$

Conclusion:

Hence, equation in slope-intercept form is $y=1.47x+14.7$

(b)

To determine

To calculate: To describe what the slope means

Answer to Problem 8.8MPS

Slope means that with every $1$ meter increase in the depth, there is $1.47$ psi increase in the pressure.

Explanation of Solution

Given information: At a depth of $30$ meters, a scuba diver

noted the pressure was $58.8$ pounds per square inch (psi). At a depth of $70$ meters, the pressure was $117.6$ psi

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Calculation:

Given that at a depth of $30$ meters, a scuba diver noted the pressure was $58.8$ pounds per square inch (psi). At a depth of $70$ meters, the pressure was $117.6$ psi

Equation to represent the data is

  $y=1.47x+14.7$

On comparing the above equation with slope-intercept form of line

  $\begin{array}{l}c=1.47\\ y=14.7\end{array}$

Here, $slope=1.47$

This means that with every $1$ meter increase in the depth, there is $1.47$ psi increase in the pressure.

Conclusion:

Hence, slope means every $1$ meter increase in the depth, there is $1.47$ psi increase in the pressure.

(c)

To determine

To calculate: To find the diver’s depth if the pressure is $107.3$ psi

Answer to Problem 8.8MPS

The diver’s depth if the pressure is $107.3$ psi is $63$ meters

Explanation of Solution

Given information: At a depth of $30$ meters, a scuba diver

noted the pressure was $58.8$ pounds per square inch (psi). At a depth of $70$ meters, the pressure was $117.6$ psi

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Calculation:

Given that at a depth of $30$ meters, a scuba diver noted the pressure was $58.8$ pounds per square inch (psi). At a depth of $70$ meters, the pressure was $117.6$ psi

Equation to represent the data is

  $y=1.47x+14.7$

Here Pressure $y=107.3$

Substituting the values,

  $\begin{array}{l}107.3=1.47x+14.7\\ 1.47x=107.3-14.7\\ 1.47x=92.6\\ x=62.99\\ x=63\end{array}$

Conclusion:

Hence, diver’s depth is $63$ meters